Many-Body Atomic Speed Sensor in Lattices

We study the properties of transmissivity of a beam of atoms traversing an optical lattices loaded with ultracold atoms. The transmission properties as function of the energy of the incident particles are strongly dependent on the quantum phase of the atoms in the lattice. In fact, in contrast to the Mott-insulator regime, the absence of an energetic gap in the spectrum of the superfluid phase enables the atoms in the optical lattice to adapt to the presence of the beam. This induces a feedback process that has a strong impact on the transmittivity of the atoms. Based on the corresponding strong dependency we propose the implementation of a speed sensor with and estimated sensitivity of $10^8 - 10^9$m/s/$\sqrt{\rm Hz}$, which we characterize via the Fisher information. We apply our findings to a bosonic $Li-Rb$ mixture, which is relevant for experiments with ultracold atoms. Applications of the presented scheme are discussed.